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# Computational Fluid Dynamics

### Overview

COURSE OUTLINE: The course deals with the numerical solution of equations governing fluid flow and would be of interest to engineers and scientists—both spiring and professional—with chemical/ mechanical/ civil/ aerospace engineering applications. In all these fields, one needs to deal extensively with fluid flow-related phenomena and one needs to resolve flow-related features of the processes and equipment. Although the equations governing fluid flow have been formulated more than 150 years ago, it is only in recent years that these are being solved in the practical applications in which the flow occurs. The course deals with the basic techniques that enable the numerical solution of these equations.

### Syllabus

Mod-01 Lec-01 Motivation for CFD and Introduction to the CFD approach.
Mod-01 Lec-02 Illustration of the CFD approach through a worked out example.
Mod-02 Lec-03 Eulerian approach, Conservation Equation, Derivation of Mass Conservation Equation.
Mod-02 Lec-04 Eulerian approach, Conservation Equation, Derivation of Mass Conservation Equation.
Mod-02 Lec-05 Forces acting on a control volume; Stress tensor;.
Mod-02 Lec-06 Kinematics of deformation in fluid flow; Stress vs strain rate relation.
Mod-02 Lec-07 Equations governing flow of incompressible flow;.
Mod-03 Lec-08 Cut out the first 30s; Spatial discretization of a simple flow domain;.
Mod-03 Lec-09 Finite difference approximation of pth order of accuracy for qth order derivative;.
Mod-03 Lec-10 One-sided high order accurate approximations,Explicit and implicit formulations.
Mod-03 Lec-11 Numerical solution of the unsteady advection equation using different finite..
Mod-03 Lec-12 Need for analysis of a discretization scheme; Concepts of consistency.
Mod-03 Lec-13 Statement of the stability problem.
Mod-03 Lec-14 Consistency and stability analysis of the unsteady diffusion equation.
Mod-03 Lec-15 Interpretation of the stability condition,Stability analysis of the generic scalar equ.
Mod-04 Lec-16 Template for the generic scalar transport equation and its extension to the solution.
Mod-04 Lec-17 Illustration of application of the template using the MacCormack scheme.
Mod-04 Lec-18 Stability limits of MacCormack scheme.
Mod-04 Lec-19 Artificial compressibility method and the streamfunction-vorticity method.
Mod-04 Lec-20 Pressur e equation method for the solution of NS equations.
Mod-04 Lec-21 Pressure-correction approach to the solution of NS equations on a staggered grid.
Mod-05 Lec-22 Need for effici ent solution of linear algebraic equations.
Mod-05 Lec-23 Direct methods for linear algebraic equations; Gaussian elimination method.
Mod-05 Lec-24 Gauss-Jordan method; LU decomposition method; TDMA and Thomas algorithm.
Mod-05 Lec-25 Basic iterative methods for linear algebraic equations: Description of point -Jacobi.
Mod-05 Lec-26 Convergence analysis of basic iterative schemes,Diagonal dominance condition.
Mod-05 Lec-27 Application to the Laplace equation.
Mod-05 Lec-28 Advanced iterative methods: Alternating Direction Implicit Method; Operator splitting.
Mod-05 Lec-30 Illustration of the Multigrid method for the Laplace equation.
Mod-06 Lec-31 Overview of the approach of numerical solution of NS equations for simple domains.
Mod-06 Lec-32 Derivation of the energy conservation equation.
Mod-06 Lec-33 Derivation of the species conservation equation; dealing with chemical reactions.
Mod-06 Lec-34 Turbulence,Characteri stics of turbulent flow,Dealing with fluctuations.
Mod-06 Lec-35 Derivation of the Reynolds -averaged Navier -Stokes equations.
Mod-06 Lec-36 Reynol ds stresses in turbulent flow,Time and length scales of turbulence.
Mod-06 Lec-37 One-equation model for turbulent flow.
Mod-06 Lec-38 Two -equation model for turbulent flow; Numerical calculation of turbulent.
Mod-06 Lec-39 Calculation of near-wall region in turbulent flow; wall function approach.
Mod-07 Lec-40 Need for special methods for dealing with irregular fl ow geometry.
Mod-07 Lec-41 Transformation of the governing equations; Illustration for the Laplace equation.
Mod-07 Lec-42 Finite volume method for complicated flow domain.
Mod-07 Lec-43 Finite volume method for the general case.
Mod-07 Lec-44 Generation of a structured grid for irregular flow domain; Algebraic methods.
Mod-07 Lec-45 Unstructured grid generation,Domain nodalization.
Mod-07 Lec-46 Delaunay triangulation method for unstructured grid generation.
Mod-07 Lec-47 Co -located grid approach for irregular geometries; Pressure correction equations.

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